The equation $3x - 2y + 5 = 0$ can be written as:

The total cost of $7$ pens and $5$ pencils is Rs. $50$,and the total cost of $5$ pens and $7$ pencils is Rs. $46$. Represent this as a pair of linear equations in two variables.

Solve the following pairs of equations by the method of elimination:
$9x + 7y = 55$
$7x + 9y = 57$

If $I$ add $1$ to each of the two given numbers,then their ratio is $1:2$. If $I$ subtract $5$ from each of the numbers,the ratio is $5:11$. Find the numbers.

$6$ students of class $X$ took part in the Ramanujan Competitive Examination. The number of girl participants is $2$ less than the number of boy participants. Find the number of girls and the number of boys who took part in the examination using a graph.

The sum of the digits of a two-digit number is $6$. The number obtained by interchanging the digits is $18$ less than the original number. Find the original number.